FractionalGeometry-Chap2

Figure 238 two real snowakes take the origin to be

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Unformatted text preview: of slightly different absolute values, we make the fern look less symmetric and so more natural. Ofcourse, these two rules alone will not prodce the bottom two fronds. These must be used together with the other rules for the fern. r s 0.30 0.34 -0.30 0.37 Rules for the θ 49◦ -50◦ bottom ϕ 49◦ -50◦ left and e f 0 1.60 0 0.44 right fronds. 70 CHAPTER 2. ITERATED FUNCTION SYSTEMS Now imagine snipping off the bottom left and right fronds and all the stem up to the bottom left frond. What remains is a copy of the fern, not much smaller than the original, rotated a little to give the fern its overall curl, and translated vertically. r s θ ϕ e f 0.85 0.85 -2.5◦ -2.5◦ 0 1.60 Rule for everything above the bottom two fronds. Combining these three rules gives the picture on the left of Fig. 2.36. Obviously, Figure 2.36: Left: fractal fern without stem. Right: fractal fern with its main pieces pulled apart. we’ve missed the bottom of the stem of the fern. But notice a consequence of fractality: if...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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